Dimensional Consistency

The dimensions (or as they are sometimes called, units) of a physical quantity are a necessary (and useful) part of its description. Recall that the fundamental units in the SI system are kilograms (to measure mass), meters (to measure length) and seconds (to measure time). Other physical quantities are also given units that are combinations of these three, such as force (measured in Newtons), energy (measured in Joules), and a host of others. These units are multiplied or divided as their magnitudes are. For example, a table 2 meters long and 1.5 meters wide has an area of 3 square meters, written 3 m². The matter of dimensional consistency simply requires that the multiplication and/or division of physical quantities provide consistent results for the dimensions as well as the numerical answer. If, for example, the product of the length by the width of the table resulted in 3 horsepower rather than 3 m², the result would be highly suspected, even though the numerical value was correct.

Here's a short table of useful dimensional relationships - I'll add to it as we go along: